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Bernhard Bierschenk 
Department of Psychology, Lund University 

Copenhagen Competence Research Centre 


This paper is about an entirely new approach to the study of knowledge. As an introductory 
remark, the classical research operations in the field of cognition are reviewed. Against this 
background, an application of David Hestenes theory of rotational dynamics is demonstrated 
with particular reference to text processing. Based on the mechanism of joints and links of the 
AaO machine, angular displacements and the control of textual movements are topologically 
presented. In the discussion, it is made evident that the presented approach carries more 
ecological validity than is reflected through all previous methodological attempts of giving a 
precise measure of attitude change in the development of text. 

Categorisation as the foundation of knowledge 

This section is about "the study of behaviour" as the ultimate foundation of concept 
development as well as the development of skills. Within cognitive psychology and the 
psychology of learning, it is a widely held opinion that both concepts and skills are 
developing as a function of awareness, which performs the task of associating facts in a 
constructive way. Neisser (1967) for example regards them as the expected outcome of the 
operating processes of association. He takes his point of departure in information processing, 
which relates to the classical research paradigm of cognition. Central to working within this 
paradigm is the following assumption: 

The function of awareness connects certain task-specific cues with some stated criteria for the 
observation of appropriate performance behaviour. 

This kind of reasoning presupposes the presence of "a law of interaction". On the basis of 
interactions, it is proposed that networks develop as an expression of mentally generated 
concepts. Thus, the origin of skills is founded in the statistical function of linearity of 
cue-relations. However, the source of this kind of thinking can be traced to the Code of 
Hamurabi (1750 BC). Depending on the degrees of deviation from this code, a subject's 
behaviour is generating the weights connected with the correct response. 

It seems to be instructive to approach the generality of the key function of this idea by relating 
the picture of Hamurabi and his God Marduk (Jaynes, 1982, p. 199) to the Turing machine as 
shown in Figure 1. In relating the unquestioned assertion that propositions are the highest 
form of knowledge (Simon, 1981) to a generalised machine concept brings the constraints of 
its underlying logic into focus. 

A first measure concerns the stipulation of "a subject" that can perform act of discrimination. 
It is immediately evident that this measure presupposes a covert "a priori condition", which 
means that the subject is placed into a conflict. It has to decide on which of two actions it 
should carry out. When asked for a decision, the subject is simultaneously asked to refer to its 

memory. Thus, it is always the behavioural foundation of a response on which the correlation 
is performed. 

The presumption, common to all forms of cognitive studies is that a hint or pointer (a finger) 
exists, that directs the response of the subject. On the first level of the model, presented by 
Elstrup Rasmussen (1997), this ability is expressed as some filter through which the real 
world is assimilated. Filtering means that only certain relations are accessible within a 
particular domain. 

Figure 1. The bicameral mind: Julian Jaynes (1976, p. 199) 

Domain of Syntax 


Determination: meros (part) — > mer+mer 
+ izo — > (verbalising — > mer+mer+izein 




P (X) => Predication of 


Interpretation and Execution: 
Marduk, God of Babylon 
=> Legislation 

Binding Law 



Working: Immediate action: Hamurabi, 

King of Babylon => Localisation of directives 


The real world is posed to the subject through its senses as a cipher. Binary valued cues are 
the carriers of real world information that has to be decoded on the basis of the messages of 
experience. It follows that cues can be used in order to establish a linear discrimination or 
"cue- structure". 

Knowledge as the functional outcome of classification 

The "study of classification" evolved from a long contemplation about the "laws of existence" 
and the "laws of the universe". Basically, classifiers are occupied with an analysis of 
experience. However, their purpose has been to come to insight and thus to "true" knowledge. 
The models presented by I. Bierschenk are demonstrations of what kind of instruments are 

available for a distinction between properties essential to real objects and properties which 
depend on the mode of classification. A prototypic machine for classification is given in 
Figure 2. 

Figure 2. Subjective determinism 



Axiomatic Classes 


Demons / Grandmother 

Linear and discrete 


Logic of Predication 


Still, the analyses of classification continue to be conducted with the purpose of 
demonstrating the Gestalt phenomenon as evidence of insight. This kind of studies pertains to 
the second level of the model developed previously (Elstrup Rasmussen, 1997). It is the basis 
for the distinctions that can be made with reference to the configurational relations between 
cues and perceived object. Such relations are designed by translating cues and categories into 
the determinism of Figure 2. Within the clarified frame of reference of predicate logic, 
structural assumptions of a statistical kind are utilised in the modelling of knowledge 
acquisition and skills. 

This kind of cue- world relation is very different from the properties and relations ascribed to 
the objects and organisms at the ability level. The cues of import in determining the statistical 
relations concern the mental world of concepts. They are constructs, which are conceived of 
as reasoned representations of the real world. Because of the absence of structural 
implications, inference and personal interpretations have had great impact on the definition of 
knowledge and skills (B. Bierschenk, 1995). 

Knowledge as the outcome of life processes 

Life is the ultimate definition of a biological machine that can produce knowledge and skills. 
In this respect, the biological machine is different from the Turing machine. Compared to the 
kind of results expected on the basis of the two preceding sections, the present is entirely 
different because it takes its departure in processes, sequences, stability and change. In 

contrast to the Turing machine, a biological machine is dependent on oscillations in its 
information pick-up. Therefore, co-ordination, directionality and co-operation are important 
concepts in the description of knowledge. Point of departure is the text building behaviour and 
the discontinuities contained in the discourse of a text. Thus, knowledge develops at the edge 
of uncertainty. Figure 3 presents this kind of machine. 

Figure 3. 






Natural Language 

=> Affinity of (AaO)-units 

=> Folding into Grapheme-strings 

Figure 3 provides the relationship that link the macroscopic "discourse" with the microscopic 
"co-ordinates" of a language space. The parallel trajectories connecting "Scanator" with 
"Natural Language" concern those physical processes that are reversible. They have the task 
of carrying out the necessary substitutions by up- and downward moves. These Ups and 
Downs have been identified with the translations of textual elements in space and time. It 
follows that a substitution process is establishing temporal symmetry relations. However, the 
number of configurational constraints remains invariant. The non-parallel trajectories, 
connecting "Natural Language" with "Discourse" on one hand and "Discourse" with 
"Scanator" on the other, have been identified with irreversible flow processes. These flows 
are associated with attitude changes. Thus, flows are changing the internal constraints of the 
system. This means that the spreading of information by means of a discourse can be equated 
with temporal asymmetries. 

Text plays the central role in the working of Figure 3. The functional units of text building are 
the AaO's. By analysing text as a dynamic system, malleable couplings of time dependent 
developments become accessible, which has been demonstrated by I. Bierschenk (1997). The 
rhythmic working of the Scanator is producing the base for the working of an optimising 
function in the clustering of textual elements. This function affords the prerequisites for the 
emergence of novel concepts, which on every level of clustering determines what one is able 
to know. 

As proposed by Elstrup Rasmussen 1996, p. 14), the "Holophor" is the kind of topological 
layout that makes explicit what the structural relation of the discourse are and how they have 
evolved during processing. This terminus relates to Pribram's (1971) language of the brain, 
where he proposed the term hologram. The other part of this term concerns the metaphoric 
quality of the analysis. Thus a "Holophor" is carrying wholeness. 

The terminus "Scanator" has been proposed as concise definition of the AaO-mechanism, 
which connects the dynamic flow-fields of language over three levels. Moreover, the terminus 
has also the function maintaining the Scandinavian origin of its methodological and 
theoretical development (B. Bierschenk, 1995, p. 9). 

In adopting the terminology of spinor mathematics, it will be shown that the AaO-units have a 
certain rotational dynamic. In the dynamics of knowing, these units have the capacity of 
developing higher-order relations of great variety. However, they can be differentiated on the 
basis of broken symmetries and topological operations. 

A scalar component in the form of radians has been introduced (B. Bierschenk, 1997). Its task 
is to give a precise definition of articulation in a discourse. It follows that the radians 
correspond to the rotations in the A- and O-component of the AaO-units. The focus on 
rotational dynamics and on a geometric description of text building behaviour provides for the 
linkages and bifurcations resulting from angular displacements. The negentropic control of 
textual movements will be discussed with reference to the discontinuities of a text example. 
On the basis of the example, time-dependent morphologies will be presented and discussed. 

Knowing as a function of co-ordinate space transformation 

The token individual is in the present context a member of a biological system that can come 
to knowing of itself and its environment. It is important to note that the biological system is 
conceived of as an abstraction. This means that it is always the individual that abides the (T <x 
M P L E ) law (Kugler & Turvey, 1987, p. 206). It follows that each individual system provides a 
unique physical context for the expression of the law. On the basis of motor task 
performances have Kugler and Turvey (1987) demonstrated the operation of the proposed 
law. Evidence of its operation in connection with text production has been given in B. 
Bierschenk (1995). Unfolding the configuration of a text implies the identification of its 
twisting and twining. Twining marks a fold in the development of a helix. Folding is initiated 
whenever a new variable enters into the process of production. However, twisting marks the 
appearance of string of graphemes, which includes the formal pronoun ('it'). The result of this 
processing is demonstrated in Figure 4. 

Figure 4. Configuration of the Double Helix 

Of the common attitude today 1 
And thatX 

And thatX 


Most people + (j35 

My salary 

My salary ^ 


Most people + Up 

local authority 

+ Money + 

With ideas as to 

Up the local 

authority + 

Money + 

With ideas as to + 

the local authority |^J3 1 

+ Money 

The local authority 
+ Money (&% X - 

Money \$}2 

Not + I + a dam: 

A damn 

It + I + a damn 

Not + and_that X + For local 

government employees only 

For local government employees only 

Most people 

Most people 

Most people 

Most people 
Most people 
Most people 
Most people 

Most people 

The local authority 

The local authority 

The same reasoning here 

Figure 4 is a demonstration of the dynamics of a text, and that dynamics is the agency through 
which linkage relations among the a's and the P's are generated, modified or broken. The 
breaking of a linkage relation is marked by the absence of an arrow. Evidently, a change in 
the linkage relation concerns a change in the set of states that is more or less significant. 

As discussed in B. Bierschenk (1993, p. 6), time enters into the calculations in two different 
ways. As a parameter, it is incorporated in the definition of a phase. This means that phase is a 
function of elapsed time. As an organising device, it plays an important role in connecting the 
direction of time with dynamic processes. Further, it concerns the degrees of displacement of 
various textual elements that must occur if the expression of particular physical processes is a 
knowing invariant. In this respect is the choice of a particular individual not arbitrary at all. 
On the contrary, the choice respects the individual as the unique frame of reference to which 
different disparities between developing forms and structures can be related. Studying 
knowing as outcome of text production is a choice that encourages the establishment of 
temporal morphologies and a concentration on the function played by geometry. 

Thus, it is clearly illustrated through Figure 4 that a making and breaking of the links between 
its elements will strongly influence the attractor states. Some point attractors will simply be 
more attractive. Crucial for the continuation of the discussion of Figure 4 is the fact that every 
circle or point represents a possible asymptotic state for the textual system. Thus, dynamic 
movements are arising from the co-operative interaction and contract on the linkage relations 
which persist on the trajectory of the A- and B-dimensions. Furthermore, each trajectory 
uniquely determines the behaviour of the respective component as well as the system in its 
entirety. In this sense, it is its dynamics that is limiting the number of degrees of freedom and 
consequently the states to be considered in the description of the system. The next step 
therefore is to ponder on the base of the textual expression, given in the form of a translation 
from a Swedish text into English. 

Just think of the common attitude today, and that does not go for local government employees 
only, most people think I have got my salary, why should I bother to come up with ideas as to 
how the local authority could save money ? I don not care a damn. It is the same reasoning 
here. (Professional translator: Dagny Persson, Lund) 

Related to this text has been the newly developed theory of rotational dynamics (Hestenes, 
1986), which in essence is the foundation on which the form, function and growth in knowing 
is discussed. This discussion entails the concept of time as the expression of successively 
increasing or decreasing rotational velocities. The results, which are the outcome of 
established constraints on set of the states are shown in the Figures 5 and 6. 

Figure 5. Holophor of the B-dimension 

Holophor of the B-dimension 


■ Series2 

■ Series5 

Series 2: Intention 
Most People + My Salary 
Physical Anchorage 
in the Tex 

{Conviction (2), Accusation (3), Disloyalty (6)} 

Series 3: Intention 
My Salary 
Physical Anchorage 
in the Text 

Series 4: Intention 


Physical Anchorage 

in the Text 

{Malfunctioning (4), Fraud (5), 

Ortodoxy (6), Prejudice (7)} <= Not a Dam 

Physical Anchorage 
in the Text 

{Appointment (2), Discontent (3), 
Sluggishness (5)} <= Money 

Physical Anchorage 
in the Text 

What matters in considering Figure 5 is that a clear distinction can be made between the 
physical thing and the model of analysis. This means that this distinction can be uphold 
against the contrary tendency of conceiving natural language from a phenomenological point 
of view, which is contaminated with naive realism. Thus, the model that has generated the 
dimension has also generated a demonstrative definition of what a concept stands for. In 
comprehending a concept, it must be related to a measuring space that is consistent with the 
Euclidean properties of a physical space. 

The co-ordinate space used in Figure 5 states the geometry structure of the textual system in a 
fixed format. However, the physical properties of the frame of reference (the token individual) 
may be obscured by the fact that a fixed format cannot account for the response surface or 
curvature of the reference space. Because the curvature of a geometric structure is usually 
time-dependent, relations among physical quantities should be represented as shown in Figure 

Compared to the original text, which is of a high-dimensional kind, its alternative topological 
description is of a low-dimensional kind. This means that two or at most three dimensions are 
sufficient for a characterisation of its significant invariants. Accordingly, the study of natural 
language production allows for the extraction of the intention and orientation of a text. With 
respect to its informational value, it is made evident, that "Malfunctioning" is the deeply 
embedded concept that gives a hint on what kind of knowing the text producer holds. 

Through the causal relationships between Figure 5 and Figure 6, it is also possible to 
determine the text producer's perspective specificity. Figure 6 demonstrates the fact of a 
perspective transformation. 

Figure 6. Holophor of the A-dimension 

Holophor of the A-dimension 

Series 2: Intention 
Most people 
Physical Anchorage 
in the Text 

Series 3: Intention 
Most people 
Physical Anchorage 
in the text 

=> {Conviction (2), Accusation (3), 

Fraud (5), Ortodoxy (6), 

Disloyalty (7)} <=I 

Physical Anchorage 
in the Text 

=> {Appointment (3), Discontent (4), 

Prejudice (7)} <= I 

Physical Anchorage 
in the text 

Series 4: Intention 


Physical Anchorage 

in the text 

=> {Sluggishness (3), 
Prejudice (7),} 


Physical Anchorage 

in the textl 


An inspection of the Holophor makes evident a high degree of similarity in the curvature of 
both dimensions. However, differences have occurred with respect to the central concepts. 
While "Malfunctioning" is the global state attractor in the preceding Holophor, now it is 
"Fraud", which has its physical anchorage in "Local authority". A further comparison shows 
that "Disloyalty" appears at a deeper conceptual level. Here, the notion "depth" refers to the 
degree of processing as well as to the fact that the concept is relational embedded in a 
"Prejudice"-factor. Prejudice appears twice and at different positions, which is indicative of a 
looping in the argumentation. 


A final comment on the presented method and its outcome concerns the conceptual 
examination, which requires the explicit formulation of all the presuppositions that can be 
differentiated. The present analysis must be distinguished from the naive realism of common 
sense approaches to text processing. The properties usually perceived and ascribed to a text 
are totally dependent on the mode of the content analytic. Thus, all the implicit assumptions 
that goes with the conventional approaches as well as the complexity of subjective experience 
distracts the social sciences from making progress in the study of mentality. 

The other line severing the study of cognition from real progress is the naivety in the 
scientific realism of psychometrics. Within this field of study and research, it is presumed that 
the real world can be known only indirectly. Moreover, it is assumed that the world can be 
represented conceptually by means of constructs. At present, constructs constitute the basis 
for the distinction between Science and Non-Science. Methodologically, however, the sharp 
distinction between these two modes has not carried social scientists far enough. Unable to 
distinguish between the physical thing and its models, social science is still restrained by the 
iron cage of the mental world concepts. 


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